Question: Simplify the following expression: $ p = \dfrac{9}{8} - \dfrac{n + 7}{-2n + 10} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-2n + 10}{-2n + 10}$ $ \dfrac{9}{8} \times \dfrac{-2n + 10}{-2n + 10} = \dfrac{-18n + 90}{-16n + 80} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{n + 7}{-2n + 10} \times \dfrac{8}{8} = \dfrac{8n + 56}{-16n + 80} $ Therefore $ p = \dfrac{-18n + 90}{-16n + 80} - \dfrac{8n + 56}{-16n + 80} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{-18n + 90 - (8n + 56) }{-16n + 80} $ Distribute the negative sign: $p = \dfrac{-18n + 90 - 8n - 56}{-16n + 80}$ $p = \dfrac{-26n + 34}{-16n + 80}$ Simplify the expression by dividing the numerator and denominator by -2: $p = \dfrac{13n - 17}{8n - 40}$